{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook is to study the ebbinhaus forgetting curves.\n",
    "Some basic knowledge is about the experiments performed by Ebin in 1880 and 1885.\n",
    "the remaining knowledge as a function of time.\n",
    "## t=[20min, 1hour, 9hrs, 1day,  2days, 6 days, 31 days] \n",
    "## p=[0.58,  0.44,  0.36,  0.33, 0.28,   0.25,   0.21]\n",
    "<img src=\"ebbin.gif\">\n",
    "Reference http://stuff4educators.com/index.php?p=1_161_Forgetting-Curve "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "His data and model are still under recent research investigating. See paper below.\n",
    "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4492928/pdf/pone.0120644.pdf\n",
    "\n",
    "Their basic conclusion is that \"We conclude that the Ebbinghaus forgetting curve has indeed been replicated\n",
    "and that it is not completely smooth but most probably shows a jump upwards starting\n",
    "at the 24 hour data point.\"\n",
    "There are two functions proposed by Ebbinhaus in 1880 and 1885. \n",
    "\n",
    "### In 1880, it is a power law function, the unit t here is in minutes.\n",
    "### $1-(1-(2/t)^{0.099})^{0.51}$\n",
    "\n",
    "### In 1885, Logrithm function.\n",
    "### $\\frac{1.84}{1.84+[\\log_{10}t]^{1.25}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# These are the parameters from Ebin's original paper\n",
    "u1=1.84\n",
    "a1=1.25\n",
    "u2=0.51\n",
    "a2=0.099"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def p1(t): # in equation here t is in unit of hours.\n",
    "        p=u1/(u1+pow(np.log10(t*60),a1))\n",
    "        p=np.round(p,2)\n",
    "        return p    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def p2(t):\n",
    "        p=1-pow(1-pow(2./t/60,a2),u2)\n",
    "        p=np.round(p,2)\n",
    "        return p    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "equation p1 [ 0.57  0.47  0.34  0.3   0.28  0.25  0.21]\n",
      "equation p2 [ 0.56  0.47  0.35  0.31  0.29  0.25  0.21]\n",
      "experiments [ 0.58  0.44  0.36  0.33  0.28  0.25  0.21]\n"
     ]
    }
   ],
   "source": [
    "t=np.array([1./3,1,9,24,48,6*24,31*24])\n",
    "control=np.array([0.58,0.44,0.36,0.33,0.28,0.25,0.21])\n",
    "print('equation p1',p1(t))\n",
    "print('equation p2',p2(t))\n",
    "print('experiments',control)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0023 0.0019\n"
     ]
    }
   ],
   "source": [
    "def error(t):    \n",
    "# calculate the sum of square error\n",
    "    error1=(p1(t)-control).dot(p1(t)-control)\n",
    "    error2=(p2(t)-control).dot(p2(t)-control)\n",
    "    return print(error1,error2)\n",
    "\n",
    "error(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0018 0.0025\n"
     ]
    }
   ],
   "source": [
    "# In the draft paper, the parameters are set differently from the original paper.\n",
    "# These are the parameters from the paper table 4. \n",
    "u1=1.8\n",
    "a1=1.21\n",
    "u2=0.523\n",
    "a2=0.101\n",
    "\n",
    "error(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## I would conclude that with power law equation u1=1.8, a1=1.21 is a better function for make error smaller.\n",
    "$\\frac{1.8}{1.8+\\log_{10}t^{1.21}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10ccbd0f0>,\n",
       " <matplotlib.lines.Line2D at 0x10ccbd2b0>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEACAYAAABbMHZzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niMQhJX8RkTik5C8iEof+Hzb9nrxlLh34AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c7d4cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1)\n",
    "plt.plot(np.log10(t), p1(t), '.r-', np.log10(t), p2(t), 'xb-')\n",
    "# redline for p1, blue line for p2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## There are two more equations with MCM function and summed exponential functions\n",
    "In page 18 of the pdf file, two other equations are.\n",
    "#### $u1*e^{t1}+u2*e^{t2}$\n",
    "\n",
    "#### $u1*e^{-a1 t1}+(e^{-a2 t}-e^{-a1 t})*\\frac{u1 u2}{a1-a2}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In table 4 and table 5 of the paper, it shows that sum of squared error is the smallest for Ebbin's model. \n",
    "\n",
    "## Therefore I suggest use Ebin's log equation\n",
    "## $p=\\frac{1.8}{1.8+[\\log_{10}t]^{1.21}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## I would suggest using the review use 1, 3, 10, 30, 90 days for one cycle.\n",
    "\n",
    "<img src=\"review.gif\">\n",
    "Ref. http://www.rm2kdev.net/tag/science/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def retention(t,u,a): # in equation here t is in unit of hours.\n",
    "        p=u/(u+pow(np.log10(t*60),a))\n",
    "        p=np.round(p,2)\n",
    "        return p  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def error(t,u,a):    \n",
    "# calculate the sum of square error\n",
    "    error=(retention(t,u,a)-control).dot(retention(t,u,a)-control)\n",
    "    return print(error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "t=np.array([1./3,1,9,24,48,6*24,31*24])\n",
    "control=np.array([0.58,0.44,0.36,0.33,0.28,0.25,0.21])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.56999999999999995"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#error(t,1.8,1.21)\n",
    "retention(0.33,1.8,1.21)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x110eaa6d8>,\n",
       " <matplotlib.lines.Line2D at 0x110eaa978>,\n",
       " <matplotlib.lines.Line2D at 0x110d9fb38>,\n",
       " <matplotlib.lines.Line2D at 0x110eb0a58>,\n",
       " <matplotlib.lines.Line2D at 0x110eb5208>]"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXkAAAEACAYAAABWLgY0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xl8lNW9+PHPNxtrCDuGQBJk07ApKmKrEpcqWC/otVat\nQluv1Wtb2/q7bbW29xJ7q9XeV+tytb0vWxWhWq9VKyioqDQXcUGsGGRL2BLCviSB7Nuc3x9nJrNk\nhkyS2ef7fr3mNfPMPMycPLXf5zzf55zvEWMMSimlElNKtBuglFIqfDTIK6VUAtMgr5RSCUyDvFJK\nJTAN8koplcA0yCulVALrMsiLyNMiclhENp1in8dFZIeIfC4iZ4W2iUoppXoqmJ78s8CVgT4UkXnA\neGPMROAO4H9C1DallFK91GWQN8asA6pPscsCYKlz3/VAloiMCk3zlFJK9UYocvI5QKXH9n7ne0op\npaJMb7wqpVQCSwvBd+wHxnpsj3G+14mIaKEcpZTqAWOM9OTfBduTF+fDnxXAIgARmQ3UGGMOB/oi\nY0zcPhYvXhz1Nmj7o9+OZGx/PLc9EdrfG1325EXkBaAQGCYie4HFQIaN1+YpY8wqEblKRHYC9cC3\ne9UipZRSIdNlkDfGfCOIfb4fmuYopZQKJb3x2g2FhYXRbkKvaPujK57bH89th/hvf29Ib/M93fox\nERPJ31NKqUQgIpgw33hVSikVhzTIK6VUAtMgr5RSCUyDvFJKJTAN8koplcA0yCulVAKLfJCvrYWP\nPrLP8SRe2x2P4uFYR6ON8XBcfMVjmxNM5MfJn3kmbNsGKSnQrx9Ij4Z+RpYx0NgIDkd8tTsexcOx\njkYb4+G4+PJsc2oq5ORAZib07w8DBng/+3uvq2fX69TUaP+lYdebcfKRD/JpadDWBunp8OabMGtW\nxH6/x9avh3nz4q/d8SgejnU02hgPx8WXb5v/8heYPBnq66GhoevnYPdJS+v+iaE7+/bpE9oTam0t\nbN4MU6fak14Q4ivIz5gBW7dCQQG8/37Qf2RU1dbCRRfFX7vjUTwc62i0MR6Oi69ItNkYaG7u3omh\nuyeTtrbgTxBd7WMM3Hkn7N4NU6YEfUziK8ifPAlbttg/MNb/I/VUWxuf7Y5H8XCso9HGeDguvuKx\nzb7a2gKfDLp7UjlyxKarwV7drF0Ls2d32YT4CvJau0Yplax6eHWjQV4ppeJFD65uNMgrpVQC0yqU\nSiml/NIgr5RSCUyDvFJKJbCggryIzBWR7SJSJiL3+Pl8sIi8KiIlIvKxiBSEvqlKKaW6q8sgLyIp\nwBPAlcAU4CYROcNnt/uAjcaYGcA3gcdD3VCllFLdF0xPfhawwxhTYYxpBV4EFvjsUwCsATDGlAL5\nIjIipC1VSinVbcEE+Ryg0mN7n/M9TyXAPwOIyCwgFxgTigYqpZTqubQQfc9DwGMi8hnwBbARaPe3\nY1FRUcfrwsJCCgsLQ9QEpZRKDMXFxRQXF4fku7qcDCUis4EiY8xc5/a9gDHGPHyKf7MHmGaMqfN5\nXydDKaVUN4V7MtQGYIKI5IlIBnAjsMKnAVkiku58/R3g/3wDvFJKqcjrMsgbY9qB7wOrgS3Ai8aY\nbSJyh4jc7tztTGCziGzDjsL54Sm+jwceuBft0SulVPhFvHbN66//lT//+VYWLnyWr371uoj9tlJK\nxau4ql2zfPnPuOOOWl599QdceukEnn1Wh9QrpVS4hGp0TdDa2hoRgebmKubPH8rpp9/DunX307dv\nPn375jkf+fTp436dljYYifX1LJVSKgZFPMg3Np5kyZICWlsrmTjxcS6++J9pbT1KU1MFTU3lNDVV\n0Ni4k+rq9zq2wdC3b54z8HueDOx2evpIPQkopZQfEQ/yCxc+y1VX/TOrVr1KRcUORISMjJFkZIxk\n0KDz/P6b1tYamprKaW6ucJ4MKjh58mOamipobq6gvb2OPn1yvU4AnieEPn1GI5L4K7orpZSvhFg0\npL29viP4u64I3CeEclpbj9OnT07Aq4E+fcaSkpJxyt8wxvDggz/jvvt+rVcNSqmI0pWhuuBwNNPU\nVOkM/OVeJ4OmpgpaWg6Snj6iI/3T+WoglzffXKWjgpRSUaFBvpccjjZaWg50OgE0N1fwt7+V8Pbb\nR5kwIYVbb3Xw7LP92L07lauvnsJ1180iLS2LtLTBpKUNJjXV/dr9flaXVwlKKXUqvQnyEc/Jx6KU\nlDT69s2lb9/cTp9Nn24455y/8uqrdyNygJSUTL73vW9SWFhAe/tJ2tpqaG7eT339VtraapyPEx2v\n29tPIJLuJ/h7nhT8nRzcr1NS+muKSCnVIxrkuyAiiKTQ2FjLkiUFNDZWMmjQ+WRnB5eyMcbgcDR0\nCv7u1/a5qamC9nZ/n9dgTGuAq4TAr733z9Qbz0olKQ3yQaio2NFpVFCwRITU1AGkpg6gTx/fCs3B\ncThaOp0UXFcJrteNjTsDnkDa22tJTR3YjZOCv6uJyKWc9Ca3UqGjOfkkYIyD9vZav1cJgV77XlWI\npAZ9QvB3AklNHRB0wH7jjZf1JrdSHvTGqworm3JqDHhSCJRm8k45tThPDoFPCq+9toXXXvuA0083\nLFx4kOefz2P37gwWLvw+3/rWXdqrV0lLg7yKeQ5Ha5cnhdbWGtasKWHduk+47bYm/vSndM4+eyDn\nntsEtJGWNpT09CGkpQ0lLW0I6enez/Zz3/eGkJKSHvK/JxopJU1jJS8dXaNiXkpKOhkZw8nIGH7K\n/crKXqat7VaWLDmd1tZKzjjjj8yZcx0ORzOtrdW0tVXR1lZNa2sVbW1VHe81Nu5wvlfd8Wz3rSEl\npW8XJwb/J47U1EEBg+nKla/wxRe/Z9Wq8yKWUorGb6r4pz15FVOefPLX5OdP8rrJ/d3v3tvj7zPG\n0N5e6xX4O58sqv1+3t7eQFraYK/Av3LlcVat2sn48cI3v1nF0qXD2bUrhWuu+RLXXXd+CI+E2yuv\nrOe11z5k/HgHixYdY9myUezencENN1zPLbcs9Eh7DdJRVAlK0zVKhYFNMdV4Bf7W1ireemsNa9a8\nyq23nuCZZzKZM+dS5syZHLYUijGG4uJS1q5dw6231vL00/254IICZs/u50x9eY6iGtCN0VP+RlH1\nCXnbNcXUe5quUSoMbIppBBkZI7zeHz68Ly0tL7NkSQHNzZWcdtpCJkwIb/pk+/aXaWlZw5IlBbS0\nVJKXdy8zZ3r/ZjCjqFpaDtHQsD3gvRGR1CBGTwU+eaSmDvQK5ppiij4N8kp1U2/mTYTzN0VSnAE4\nC8jr9m+4R1Gdelhtc/O+gCcSh6OJtLQs3nlHePfdOsaPT+GOOxpZsuTbPPTQbcyfP5PrrptNamp/\nUlIGkJran9TUAaSkeD/7fi6SoVcCPaTpGqVUyHiOonrjjVdYteq3fOtbR3n22aFcfvl1zJlzBg5H\nAw5HA+3t9R3P7e0NOBz22fN9+9yAMW3dPjHY94P9N/0idj+jJymssKdrRGQu8Ch2ucCnjTEP+3w+\nDPgzkA2kAr81xizpSYOUUvHLcxRV//7jaWpqYsmSApqaKhk69Epyc3uWsnE4WnE4Grt1YmhpOdyN\nk0kjKSl9fE4C3TmZdP1vXFcjkU5hddmTF5EUoAy4DDgAbABuNMZs99hnMdDXGPMzERkOlAKjjDFt\nPt+lPXmlkkSoR0qFk01VNfk5WXR9Mgn236xe3caaNcKECcKtt7bzwgsT2b07nYULf8C3vnXHKdsX\n7p78LGCHMabC+WMvAguA7R77HAKmOV9nAsd9A7xSKrl873s/63gd6zddbY2pfqSm9gvbb1x4YQuz\nZr3Aa6/9HJEDtLc3cffdD4b92KQEsU8OUOmxvc/5nqc/AlNE5ABQAvwwNM1TSqnEkJqaQWrqwI6K\ntvX1Nc4qt+G9oRyq0TU/A0qMMZeIyHjgHRGZboyp892xqKio43VhYSGFhYUhaoJSSsW2YEdmFRcX\nU1xcHJLfDCYnPxsoMsbMdW7fCxjPm68isgp4wBjzgXP7PeAeY8ynPt+lOXmllOqm3uTkg0nXbAAm\niEieiGQANwIrfPbZBlzubMwoYBKwuycNUkopFTpdpmuMMe0i8n1gNe4hlNtE5A77sXkK+DXwrIiU\nAAL81BhTFc6GK6WU6ppOhlJKqRgX7nSNUkqpOBWVIF9cXhyNn1VKqaSjQV4ppRJYxKtQHm84zrJN\ny2hobWDGqBnMOG0Gk4dNJj019Eu0KaVUsot4kP/dR79jd/VuPj3wKW+UvUFtSy3HG45zxvAzmHHa\nDBv4ncF/aL+hkW6eUkollKiMrikqLqKosKjj/fqWejYf2UzJ4RJKDpVQcriETYc3kdU3yyvozxg1\ngwlDJ5CaokucKaWSR9yvDDUgYwDnjzmf88e418h0GAflNeUdQf8vm//Cve/ey+H6w0wZMcUr8E8f\nNZ2svllR/AuUUio2RaUnX1xeTGF+YY++42TzSTYd3tQR/EsOl7DlyBZGDBjRqdc/bsg4UkRHiSql\n4lvSL+Td7mhnV/Uur8BfcqiEmqYapo2a5hX8p42cxoCMASFvg1JKhUvSB/lAqhqrOvX6tx3dxphB\nYzrd5B07aGyXJT97cwWilFI9pUG+G9ocbZQeK/W6yVtyuISmtqaOoD991HRmnDaDKSOm0C/dvYiA\n7w1jpZSKBA3yIXCk/ojXyJ6SwyWUHS9j3OBxHb3+TYc3cX/h/YwbMo60lJi4Z62USgIa5MOkpb2F\npSVLWVm2kkN1h/h4/8dk9cmirqWOnMwcZo6eyeRhk+1juH0e1n9YtJutlEowGuQjxJWuaWxtZGfV\nTkqPl1J6rJTS46VsP7ad0uOlpKekM3n4ZM4YdkZH4J88fDLjh4zXWb1KqR6J+3Hy8aZfej+mjZrG\ntFHTvN43xnC4/nBH4C89VsrairVsP7adfSf3kZuV6w78wyZzxnB7IhjRf0TY13lUSiUn7cl3Q29G\n1zS3NbOrepf7BOA8CWw/th2D8Ur5uF5PGDqBvml9Q/tHKKXijqZr4pgxhmMNx7xSP67X5TXl5AzK\n6ZT3nzx8MtkDs7X3r1SS0CCfoFrbW9lTs8fm+31OAE1tTUwaNsmmfDxOABOHTaR/ev9oN10pFUIa\n5JNQdWO1V8rHdQLYXb2bkQNGdsr7Tx42mZxBOVrmQak4FPYgLyJzgUdxL+T9sM/nPwZuBgyQDpwJ\nDDfG1Pjsp0E+zNod7ZTXlPsd+VPbXMvEYRP9pn8GZgyMdtOVUgGENciLSApQBlwGHAA2ADcaY7YH\n2P9q4EfGmMv9fKZBPopONJ2g7HhZp/z/juM7GNpvaKcbv5OHTSY3K1dLOysVZeEO8rOBxcaYec7t\newHj25v32P95YI0x5mk/n2mQj0EO42Dvib1eQz9dJ4DjDccZP3S8O/fvcQLQ8s5KRUa4g/x1wJXG\nmNud27cAs4wxP/Czbz9gHzDeN1Xj/FyDfJypa6mzvX+fG79lx8sYmDGwI+B73gDOH5yvZR+UCqFY\nmgz1T8A6fwHepaioqON1YWEhhYWFIW6CCqWBGQOZmT2Tmdkzvd43xrC/dr/Xjd+3d71N6bFSDtUd\n4vQhp/ud+BXsko5a8VMls+LiYoqLi0PyXcGma4qMMXOd2wHTNSLyKvCSMebFAN+lPfkk0NjayI6q\nHZ1u/JYeK6VPWh+/N359yz5oxU+l3MKdrkkFSrE3Xg8CnwA3GWO2+eyXBewGxhhjGgN8lwb5JGaM\n4VDdIb8jf/af3E9uVm5H2mf7se3cfcHdjB8ynjGDxujNX5XUIjWE8jHcQygfEpE7sD36p5z7fBOb\nu//GKb5Hg7zyq7mtmRe+eIG3dr7FsYZjrClfQ+6gXKqaqmhua+b0Iaczfuh4xg9xPpyvxw0Zp6Uf\nVMLTyVAq4XimaxpaG9hdvZtdVbvYVb3L/Vy9i70n9jJywMhOwd/1PKTfkOj+IUqFQCzdeFUq5Pqn\n92fqyKlMHTm102dtjjYqT1R6Bf+Xtr7U8To9Jb0j4E8YOsHrBJCdma0zgFXC0568ikmhGF1jjOFo\nw1GvK4Cd1Ts7tmubaxk3ZJzfq4D8wflkpGaEvY1KBUPTNUr1QG1zrU0D+aSAdlXtYn/tfrIHZne6\nD+C6Gsjsk6kjgFTExG2Qr6mBDz6Ar341Yk1QKiit7a1UnKjwex9gV9UuBmYMJC0ljXNHn8tpA08j\ne2A22ZnZXs+jBo7q8mqgu/TqITnFVU6+pgYGD7bPP/85PPBApFugVNfSU9OZMHQCE4ZO8Hq/uLyY\nv+/5O3Utdfzu49/RP70/+0/up6mtiQO1BzhUf4iDtQc5WHeQI/VHyOqT1Sn4+zspBFsgToO86q6I\nB/mf/xzuvBP+8Acb4AcPjnQLlOq5wvzCjiCb2SfzlOmadkc7xxqOcajuEAfrDnYE/93Vu/mg8oOO\n7YO1B0lNSe0c/J2vPd/XdKfqrogH+UWLYNo0uOoqWLcOrrwS0nV9a5WAUlNSGTVwFKMGjmIGMwLu\nZ4yhtqXWK+gfrDvIobpDbD66ma1HtrL35F7qmutoam/iyQ1PktU3i4LhBVww9gLysvLIG5xH/uB8\nsgdm68Qx5SXiOfnvftdw++3wwx9CUxPs2QM33WSD/9lng65op+JFNFIn9713H7dMv4XymnIqaiqo\nOGEfru3jjcfJycwhf3A+eYPz7AkgK69je8ygMSG/T6DCL65uvFZXG6+c/L/8C6xYAUuXQr9+Ntjf\nfDOMGROxZikVN7oa0dPU1kTliUob/Gs8TgDO7QO1Bxg1cFRH77/jBOCx3S+9X+T+IBWUuArygUbX\nGGNfL10KL78M55xjA/6118JAXbRIKaD3Vw9tjjb2n9zfEfQ7TgDOk0HliUqy+ma5U0BZ+d4ng8F5\nDOozKKJtVnEc5ANpbITXX7cBf906WLDABvzCQkjVdKNSYeMwDg7XHfbq/fteDaSnprt7/x73A1yv\nh/UbhnjkXXU+Qe8lXJD3dPgwvPiiDfhHjthUzqJFUFAQpkYqpQIyxnC88bh38Pe5N9Da3up1P2BH\n1Q5um3lbx9XAqIGjtJxENyV0kPe0eTMsWwZ//jNkZ9tgf9NNMGJECBuplOqVk80neXnLy7y7511q\nmmp4c+ebFAwvoKaphoa2BhpbG8nNyg2YDsrJzNERQj6SJsi7tLfDmjW2d//663DxxTbgX3019NWq\ns0rFFN90TUNrA3tP7PW6CnClg8pryjnWcIzRmaO9bgp7jhYamzU26UYIJV2Q91RbC6++anv4GzfC\n9dfDwoXwpS/pcEylYkF3c/LNbc1Unqz0ewKoqKngYN1BRvQf4RX4PU8GuVm5CTdCKKmDvKfKSnj+\neXjuOWhttcF+4UI4/fSw/aRSqguhHl3jOULIFfg9Rwm5Rgh5XQX43CDO7JMZsvZEggZ5H8bAP/5h\n0zkvvgiTJ9t0zvXXaxkFpRKdwzg4VHcoYDqooqaCfun9Og0T9TwZDOk7xGuEULRpkD+FlhZ46y0b\n8N9915ZRWLQIrrhCyykolYxc6wz4jhAqP+G+KgC8A7/PfYGRA0b26iTQ3asbDfJBqq6Gl16yAX/n\nTi2noJTqzBhDTVNNpyGinlcDrhFC/lJB+YPzu1x1rLv3KSK1kPejuBfyftjPPoXAI0A6cNQYc4mf\nfWJm0ZAdO+xQzKVLYcAAdzmFnJxot0wpFetqm2vdI4T8pIOqm6oZO2is3xvDeYPzeGbjM/zykl8G\n/XthDfIikgKUAZcBB4ANwI3GmO0e+2QBHwJXGGP2i8hwY8wxP98VM0HexeFwl1N45RU491x3OYUB\nA2DlSvjyl71z+brYiVLqVBpbG9l7Yq9X4P9k/yeUHi+lpqmG2pZaFs9ZDHiXrw4k3EF+NrDYGDPP\nuX0vYDx78yJyJ5BtjPmPLr4r5oK8J89yCh98YMspXHstvP02PPhg58VO9CauUqonIpmuCWZucQ5Q\n6bG9z/mep0nAUBH5u4hsEJGFPWlMtPXrB1//OrzxBmzfDmedBfffD8uXw2WXwapVcN99GuCVUvEj\nVIuGpAEzgUuBAcBHIvKRMWan745FRUUdrwsLCyksLAxRE0Jr1Cj40Y/s44sv4IknbHomJwfS0mwv\n/+KLdYSOUqr7ukrPFBcXU1xcHJLfCjZdU2SMmevc9peuuQfoa4y537n9J+BNY8wrPt8V0+maQFwp\nmh//GH72M5g4EVavhrIymDsX5s+HefO0d6+UCo9wp2s2ABNEJE9EMoAbgRU++ywHLhSRVBHpD5wP\nbOtJg2KNZw5+3Dj4n/+Bqiqbp9+6FS69FF54AXJz4fLL4fHHobw82q1WSimrO0MoH8M9hPIhEbkD\n26N/yrnPj4FvA+3AH40x/+3ne+KuJx/s6Jr6enjnHbvK1Rtv2CqZ8+fbxznnQIpWVlVK9ZBOhoox\n7e3w8cc24K9YASdPwj/9kw34l16qlTKVUt2jQT7GlZW5A35JiR2ps2CBvRIYPjzarVNKxToN8nHk\n2DE7FHP5cltLZ/p028NfsAAmTYp265RSsSi+gvzJk/D553YQemZ8lfsMtaYm+Pvf3b38zEx3Hv+C\nC3Q9W6WUFV9BvqDADkvJzbUD0Ad1b+X3ROVwwGefuQP+/v12pav58+ErX4GBA6PdQqVUtMRXkE9L\ng7Y2+8asWbZK2MSJEWtDvCgvtyUWVqyA9evhootsSufqq2H06Gi3TikVSeEeJx9aU6bYaaKuZPQF\nF8DixbZwjOqQnw933WWHZVZW2hWuioth6lR7bvzVr2DTJrtAilJKBRKdnPyWLTbYZ2bCvn1w9912\ngdYnnrBTSFVAra3w/vu2h798uX3PlcfXMgtKJab4StcE+r0334Tvf9+u4PHoozBmTMTaFa+Mgc2b\n3QF/5053mYW5c7XMglKJIjGCPNiUzUMPwZNP2nKPd92lXdNuOHDAzrZdsQLWrrVpnQUL7ESs/Pxo\nt04p1VOJE+RdduyA730PDh2CP/zB1hVQ3VJfb4uoucosjB5tA/78+TBzppZZUCqeJF6QB5uL+Otf\n4f/9P7v69sMP6/TQHnKVWVi+3Ab92lots6BUPEnMIO9y8qQdffPCC7YU5K23aje0l0pL7fDM5cvt\nCJ3LL7cBX8ssKBWbEjvIu3z+Odx5J4jYFM6MGaFtXJI6etSWWVixwpZZmDHDPVpHyywoFRuSI8iD\nnRb69NO2wPstt9i1+ZK8NEIoNTXBmjXuWbeDBrnz+LNna5kFpaIleYK8y9GjcM899s7iI4/A175m\ne/gqZBwO+Mc/3AH/4EGbzlmwwJZZGDAg2i1UKnkkX5B3WbfOpnBycuxEqgkTQvfdykt5uTvgf/KJ\nnXg1f769gZudHe3WKZXYkjfIg50C+vjj8Otf28lU996rw0XCrKYG3nrLBvw337S5e1cef+pUvahS\nKtSSO8i7VFbCj35kV+V48kk77FKFXUuLd5mFlBR3wL/oIp3LplQoaJD3tGqVnSk7c6Ytj5CTE97f\nUx2MsdWjXWkdV5mFBQvsc1ZWtFuoVHwKexVKEZkrIttFpExE7vHz+RwRqRGRz5yPX/SkMSFx1VW2\noMuZZ9rxgI884i5trMJKxBYX/cUvbN5+82aYMweWLoWxY+0N2//+b6ioiHZLlUoeXfbkRSQFKAMu\nAw4AG4AbjTHbPfaZA/ybMWZ+F98V2eX/yspseYQjR+zY+i99KXK/rbzU1dmyycuXw8qV9gLLldY5\n5xx7gli50law8CysVlMDH3xgR/YolazC3ZOfBewwxlQYY1qBF4EF/trRkwaE1aRJdpjlfffB9dfD\nbbfB8ePRblVSGjgQrr0WliyxJYmeeMKOy7/5Zltw9M47oaHB3jevqbH/pqbGTonQ0kVK9VwwQT4H\nqPTY3ud8z9cFIvK5iKwUkYKQtC4UROCGG+ySgwMGQEGBnVDlcES7ZUkrNRUuvBB+8xtbYmHNGjj9\ndDtI6oUXbM/+4YfhX/8VfvlLLZmsVG8Ek665DrjSGHO7c/sWYJYx5gce+wwEHMaYBhGZBzxmjOk0\nKV5EzOLFizu2CwsLKSwsDMkfErSNG223MTXVpnCmT4/s76tTOnoUnnsOfvITyMuzF15nnw3nngvn\nnWefJ0zQYZoqsRUXF1NcXNyxff/994dvdI2IzAaKjDFzndv3AsYY8/Ap/s0e4BxjTJXP+5HNyQfi\ncMCf/mTvEC5cCEVFWh4hRrhSND/5CfzXf9nnnTthwwb49FP7XFtrg71n4B87VgO/SlxhHUIpIqlA\nKfbG60HgE+AmY8w2j31GGWMOO1/PAl4yxuT7+a7YCPIuR4/CT39qK3M98ghcd51GiihyBfgHHrAp\nGt9tl8OH3QHf9QzugO96HjUqOn+HUqEW9nHyIjIXeAybw3/aGPOQiNyB7dE/JSLfA+4EWoFG4G5j\nzHo/3xNbQd7l/fdtCmfMGC2PEEU9HV1jjF0qeMMGd+D/9FN7ceYZ+M85B4YMCf/foVSo6WSoUGht\nhcces8sP3nWXLYCm5RHiljGwa5d34N+4EU47zTvwz5ypxdZU7NMgH0qu8gibNtnyCFdcEe0WqRBp\nb4ft273TPJs3w7hx3oF/xgzo08f/d+hYfhUNGuTDYdUqW/DsvPPgd7+zxdU3b7YVuPQmbcJoabH/\ns3oG/rIyO2HaM/BPmQJpacHfN1AqlDTIh0tjIzz4IPz+9zZ1c+SI/X/7++9roE9gDQ22zp1n4K+s\ntKNtzzvPngDWroVf/Qp++1sN8Cr8NMiH24svwje+YRO9KSnw/PNw443RbpWKoJMn4bPP3IH/ww/t\nzd5zz7XVMs4+2+b3zzxTK2+q0NMgH261tbZu7pYtdnhGSgrk5sKiRTbY6+rXScWVovnOd+wa8+ee\nC9u22Ru7e/faSdUzZ7oD/7Rp0K9ftFut4pkG+UiorbVBfsoU6N8f3nvPlld84w0oLLQB/6tfDXzH\nTiWErnLydXX2nv1nn9nHxo22dMP48d6B/6yz7G0epYKhQT6aamvhlVdswN+0yRZCW7TIrnytE6sS\nTk9G1zQ32/6BZ+DftAlGj/YO/GefDSNGhOY3VWLRIB8r9u61+frnnrPj9RYtgltusWP0lPLQ1mZ7\n+Bs3ugPFLeuqAAAQZ0lEQVT/xo32fr5n4HeN4//FL3RETzLTIB9rjLF355YutTdtCwpswP/a13R5\nJBWQwwF79rgDv+thjM3r19TAt78NH31kF18ZNizaLVaRokE+lrW02NWuly61efx582xRtCuusAOv\nlToFY+DAARv433vPrmg5dqytzllQYCduuR7Tp2vPPlFpkI8XVVXw0ks24O/ebYdlLlpk/x+q+Xt1\nCr7VOe+5x47dLymxj02b7Pq6w4d7B/4ZM2yt/pSgFvpUsUqDfDzasQOWLbOPzEwb7L/xDXs3TikP\nwc6ydThsvR5X4Hc9qqpsumf6dHfgnzZN5/PFEw3y8czhgHXrbO/+1Vdh1iwb8K+5xg7VVEmvt6Nr\nqqttT98z8G/davsTvr3+vDy9qIxFGuQTRWOjXel62TI7pfKaa2zAnzNHr7dVSLW12Ro9numekhKo\nr/fu8c+YYcs16WSu6NIgn4gOHYK//MX28Kuq7FDMhQvhjDOi3TKVwI4e7dzrLy2F/PzOvf7RowP3\n+nVsf2hpkE90mzbZ3v3zz9uhFYsW2cXJtZyCioCWFlui2TfX73C4R/W4An9BgZ30rdU6Q0uDfLJo\na3OXU1i5Ei65xPbutZyCijBj7MWmb+DfvdsurDZjBkyaZKeL/Pu/w7PP2oKuGuB7RoN8Mjp50l1O\n4Ysv4Otftz3888/XO2cqapqa7E1dV9D/+GNYv95W6s7Ptzd2fZ/z8iA7W287nYoG+WRXUeEup2CM\nu5xCfn60W6aSmOfY/gcftLN1q6rsf67l5fbZ9bqmxi6x7O8EkJ8POTnJPXcwUgt5P4p7Ie+HA+x3\nHvAhcIMx5lU/n2uQDydjbMHzpUvhf//XVsx0lVPQkocqgrqbk29stKWfPAO/5/ORI7a37xn4PZ/H\njk3sjGVYg7yIpABlwGXAAWADcKMxZruf/d4BGoFnNMhHWUuLXcJw6VJYs8aWU1i0CL7yleTuEqmI\nCPXompYWu0iLvxNARQXs32/HIfi7CnC9judpJ+EO8rOBxcaYec7tewHj25sXkR8CLcB5wBsa5GPI\n8eO2Z79smf1/hmc5BaUSQHu7rfHjmwZyPVdW2hm+/q4CXM+xfLEb7iB/HXClMeZ25/YtwCxjzA88\n9hkNPG+MuUREngVe1yAfo8rK3OUUsrLc5RSys6PdMqXCxuGwKR/fqwDPk0J6euB7Anl5MHRo9MY0\n9CbIh+q6/VHgHo/tgI0pKirqeF1YWEhhYWGImqCCMmkS/Od/wv332wXJly61g5vPP1/LKaiElZIC\np51mH7Nnd/7cGHvB63sCKC52v25vD3xPID8fRo489UmgOyms4uJiiouLe/dHOwWbrikyxsx1bndK\n14jIbtdLYDhQD9xujFnh813ak49FDQ22nMLSpXbM27XX2oB/8cU6rk0ppxMnAl8FlJfbpR9zcwNf\nDfTrB//xHz2bIBbudE0qUIq98XoQ+AS4yRizLcD+mq6JZwcPusspVFfbyVYLF8LkydFumVIxrb7e\nHfT9nQyOH7dZ0bY2O9r51VeDnwEcqSGUj+EeQvmQiNyB7dE/5bPvM+iN18RQUuIup5CXZ4P9jTfq\nkkRK9UBTk70BvH69/b/Snj3BT2XRyVAqvNra4N13be9+1SpbTmHRIrjqqsQenKxUiPku/hIzPflQ\n0SCfAHzLKdxwgw34s2ZpOQWlTqE3Rds0yKvoKC+3qZylS+22q5xCXl5Um6VULOrNBDEN8iq6jIFP\nPnGXU5g6VcspKBVCGuRV7GhudpdT+Pvfbd5+0SK4/HItp6BUD2mQV7HJVU5h6VI7hkzLKSjVIxrk\nVewrLXWXUxg8WMspKNUNGuRV/HA4YO1a27v/29/sHPNFi2DBAi2noFQAGuRVfGpogNdeswF//Xp3\nOYWzz7bLC02daksHKpXkNMir+HfwILzwAjzzDOzYYatBjRtng7/OsFVJToO8ShwffWQLo7W12e3+\n/eGyy+CKK+xj4kSddKWSTm+CvJYYVLFl6lS7bGF6uh2Fs2UL3HwzbNwIl15qe/e33w4vv2wLqCml\nTkl78ir21Nba4D5lindO3hjYtg1Wr7aPdetsLfwrroArr7SlFdLTo9dupcJE0zUqOTU32znhrqC/\ne7ctnuZK7YwfH+0WKhUSGuSVAru+2zvvuIN+//7uXv4ll9jlDpWKQxrklfJlDGze7A74H35oc/yu\nXv6552qZBRU3NMgr1ZXGRpvDX70a3n4b9u2zN3JdQT/Y1RuUigIN8kp118GD7tTOO+/YVM6VV9qA\nX1iok7BUTNEgr1RvOBywaZM7tbN+Pcyc6e7lz5wJqanRbqVKYpFa4/VR3Gu8Puzz+XzgPwEH0A78\n1Bizxs/3aJBXsa++3tbXcQX9w4e9J2SNHWuHeW7erKUXVESENciLSApQBlwGHAA2ADcaY7Z77NPf\nGNPgfD0N+JsxZoKf79Igr+LPvn3eqZ1hw6Cqyk7GmjjR9vx1cRQVRuEO8rOBxcaYec7tewHj25v3\n2P8C4BFjzGw/n2mQV/HN4YAlS+A737GvwfbkZ82yhdVmzrSPiRMhRSeUq9AId1mDHKDSY3uf8z3f\nRlwjItuAVcAPetIYpWJeSgpcfz1Mm+YuvfDZZ/Bv/2br5L/yCsybZ2/kXngh3HUXPPsslJRAa2u0\nW6+SUDA9+euAK40xtzu3bwFmGWP8BnIRuRCbt5/s5zPtyavEEKj0gkt1NXz+uT0BbNxon8vLbRmG\nmTPdvf7p06Ffv4g3X8WX3vTkg5kNsh/I9dge43zPL2PMOhFJE5Fhxpjjvp8XFRV1vC4sLKSwsDDo\nxioVMzIz7YIngQwZYmfZXnKJ+736ejuK57PP4B//gD/+EbZvh9NP9w78Z52ls3OTXHFxMcXFxSH5\nrmB68qlAKfbG60HgE+AmY8w2j33GG2N2OV/PBP5qjOlUOER78kr5aGmxVwSePf5Nm+C007wD/9ln\n2x6/juhJSpEaQvkY7iGUD4nIHdgbsE+JyE+BRUALUA/cbYz51M/3aJBXqivt7VBW5h34P/vMXgm0\nt8OIEfCb39griQkTdAx/EtDJUEolug8/hDlz7GIqKSn2pm5lpS3KNmWKvQHsekyfrkM6E4wGeaUS\nXW0tXHSRXfu2oADef9+mbE6etOmdkhL38+bNMHKkDfaewX/cOB3WGac0yCuVDLoa0ePS3g67dtmA\n7/moqbFDPz0D/7RpMGBA5P4G1SMa5JVSXauqcvf2XY9t22DMGO/AP2OGLd2ga+nGDA3ySqmeaWuD\n0lLvwL9pEzQ1udM9rucpU3RMf5RokFdKhdaRI517/WVlNq/v2+vPztZef5hpkFdKhV9Li03v+Ob6\noXPgP/NMyMjQap0hokFeKRUdxtgFWHwD/549diH1/fvtCKC8PHj9dRv8dYRPt2mQV0rFlsZGePFF\nuO02W61TBIYPh4YGG+gLCuzD9XrcOJ3UdQoa5JVSscff2H6Hw6Z8tm71fhw5ApMmuYO/6zF+vK32\nmeQ0yCulYlOwY/vr6uwoH9/gv2+fLeDmG/wnTYI+fSL3d0SZBnmlVGJqbLSjerZu9b4C2LMHcnM7\np33OOAP69492q0NOg7xSKrm0tMDOnd69/m3b7AkhO7tzz//MM+N6dI8GeaWUAju5a8+ezmmf7dth\n6FD/wX/o0Gi3uksa5JVS6lQcDti7t3Pw37rV1u7xTPm4HiNGxMwkLw3ySinVE8bYsfy+Of8tW+x4\nfn89/9GjIx78NcgrpVQoGWOHdfrm/LdutTeDfYN/QYEt6hamiV4a5JVSKlKOH/c/1r+mxo7u8Q3+\nvhO9elDqQYO8UkpF24kT9gavb/A/fNg90Wv8eFi2zKaIpkxxL/7SBQ3ySikVq+rrbfDftg1Wr4Y/\n/9mmg9LTYe1au1ZvFyK1kPejuBfyftjn828A9zg3a4E7jTFf+PkeDfJKqeQVaBnHLvQmyHd5l0BE\nUoAngCuBKcBNInKGz267gYuNMTOAXwF/7EljYl1xcXG0m9Ar2v7oiuf2x3PbIYban5lpA/vatUEH\n+N4K5lbwLGCHMabCGNMKvAgs8NzBGPOxMeaEc/NjICe0zYwNMfMfSg9p+6Mrntsfz22HGGt/ZqZN\n0URoBm4wQT4HqPTY3sepg/htwJu9aZRSSqnQSAvll4nIJcC3gQtD+b1KKaV6pssbryIyGygyxsx1\nbt8LGD83X6cDrwBzjTG7AnyX3nVVSqke6OmN12B68huACSKSBxwEbgRu8txBRHKxAX5hoADfm0Yq\npZTqmS6DvDGmXUS+D6zGPYRym4jcYT82TwH/DgwFfi8iArQaY2aFs+FKKaW6FtHJUEoppSIrrMum\ni8gQEVktIqUi8raIZAXYr1xESkRko4h8Es42BUNE5orIdhEpE5F7AuzzuIjsEJHPReSsSLcxkK7a\nLiJzRKRGRD5zPn4RjXYGIiJPi8hhEdl0in1i8thD1+2P5eMvImNEZI2IbBGRL0TkBwH2i8njH0z7\nY/z49xGR9c44uEVEHgywX/eOvzEmbA/gYeCnztf3AA8F2G83MCScbelGm1OAnUAekA58Dpzhs888\nYKXz9fnAx9FudzfaPgdYEe22nuJvuBA4C9gU4POYPPbdaH/MHn/gNOAs5+uBQGm8/LffjfbH7PF3\ntq+/8zkVO+foy709/mHtyWMnTT3nfP0ccE2A/YQwX1V0Q5eTv5zbSwGMMeuBLBEZFdlm+hVM28Ee\n75hkjFkHVJ9il1g99kBQ7YcYPf7GmEPGmM+dr+uAbXSeExOzxz/I9kOMHn8AY0yD82UfbEz0/W+p\n28c/3IF1pDHmsLNBh4CRAfYzwDsiskFEvhPmNnUlmMlfvvvs97NPNAQ7ce0C56XeShEpiEzTQiZW\nj313xPzxF5F87BXJep+P4uL4n6L9EMPHX0RSRGQjcAgoNsZs9dml28e/15OhROQdwPNMItig7S/X\nFegu75eNMQdFZAQ22G9z9ohU6P0DyDXGNIjIPOA1YFKU25RMYv74i8hA4GXgh84ecVzpov0xffyN\nMQ7gbBEZBKwWkTnGmP/rzXf2uidvjPmKMWa6x2Oa83kFcNh1KSEipwFHAnzHQefzUeBv2LRDtOwH\ncj22xzjf891nbBf7REOXbTfG1LkuCY0xbwLpIhL7Kxm7xeqxD0qsH38RScMGyGXGmOV+donp499V\n+2P9+LsYY04CK4FzfT7q9vEPd7pmBfAt5+tvAp0Ouoj0d555EZEBwBXA5jC361Q6Jn+JSAZ28tcK\nn31WAIugY0ZwjSstFWVdtt0zfycis7DDaKsi28wuCYHzprF67D0FbH8cHP9ngK3GmMcCfB7rx/+U\n7Y/l4y8iw10jEEWkH/AV7OAJT90+/iGtXePHw8BLInIrUAF83dm4bOCPxpirsamev4kteZAGPG+M\nWR3mdgVkgpj8ZYxZJSJXichOoB5bryfqgmk78DURuRNoBRqBG6LX4s5E5AWgEBgmInuBxUAGMX7s\nXbpqPzF8/EXky8DNwBfOvLAB7sOO1or54x9M+4nh4w9kA8+JiGsgyjJjzHu9jT06GUoppRJYrAxb\nVEopFQYa5JVSKoFpkFdKqQSmQV4ppRKYBnmllEpgGuSVUiqBaZBXSqkEpkFeKaUS2P8HS9c2bgRA\nye8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110e62a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.log10(t), retention(t,1.8,1.21), '.r-', np.log10(t), retention(t,2.5,0.9), 'xb-'\n",
    "         ,np.log10(t), retention(t,4.0,0.6), '+g-', np.log10(t), retention(t,8.0,0.4), '*y-' \n",
    "         ,np.log10(t), retention(t,20.0,0.1), '.r-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10ed87160>,\n",
       " <matplotlib.lines.Line2D at 0x10ed87400>]"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXkAAAEACAYAAABWLgY0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ntCgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ec9b8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.log10(t), retention(t,1.8,1.21), '.r-', np.log10(t), retention(t,3,0.6), 'xb-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.31\n",
      "0.44\n",
      "0.63\n",
      "0.81\n",
      "0.94\n"
     ]
    }
   ],
   "source": [
    "print(retention(24,1.8,1.21))\n",
    "print(retention(3*24,2.5,0.9))\n",
    "print(retention(10*24,4,0.6))\n",
    "print(retention(30*24,8,0.4))\n",
    "print(retention(60*24,20,0.1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x110fb7a20>]"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEACAYAAABI5zaHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110978ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=[1,3,10,30,60]\n",
    "y=[0.31,0.44,0.63,0.81,0.94]\n",
    "plt.plot(x, y, '.r-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
